The invention relates to a roller bearing in which cylindrical rollers or tapered rollers are used as rolling elements, and particularly to a roller bearing that is suitably used in a portion to which a heavy load or a high momentum load is applied.
In a cylindrical roller bearing or a tapered roller bearing, a crowning process is applied to the rolling surfaces of the rollers and the raceway surfaces of the inner and outer races, so that the edge load which acts under load conditions between end portions of the roller rolling surface and the raceway surfaces can be reduced.
The crowning process is applied to the generating line of the rolling surface of each roller or the raceway surface of the inner or outer race so that the outer diameter of each end portion is slightly smaller than that of the center portion. Conventionally, a trapezoid or a simple circular arc is practically used as the crowning shape (the shape of the profile line to the direction of the generating line).
When a load or a momentum acting on a bearing is excessively heavy, the contact surface pressure between a roller and the bearing ring is raised to increase the internal stress. Therefore, the above-mentioned crowning shape such as a trapezoid or a simple circular arc fails to effectively reduce the edge load, with the result that the life period of the bearing is shortened.
A method in which crowning to a shape of a logarithmic curve based on the elastic contact theory is employed may be applied on such a bearing to which a heavy load or a high momentum load is applied. As one of crowning shapes used in such a method, known is a crowning shape based on the following Lundberg's expression: EQU Zp(x)={(1-.nu..sub.1.sup.2)/E.sub.1 +(1-.nu..sub.2.sup.2)/E.sub.2 }Q.sub.d.times.log{1-(2x/l.sub.a).sup.2 }.sup.-1 /(.pi..multidot.l.sub.a) (1)
In the expression, Zp(x) indicates the size of a gap between the rolling surface of a roller and the raceway surface of the inner or outer race, in the bearing radial direction (z-direction) at a position in the direction of the common generating line (x-direction) in a state where the rolling surface and the raceway surface are contacted with each other in an unloaded condition. The origin of the x-axis is set at the center in the axial direction of the roller. In the expression,
E.sub.1 : Young's modulus of the roller PA1 E.sub.2 : Young's modulus of the inner or outer race PA1 .nu..sub.1 : Poisson's ratio of the roller PA1 .nu..sub.2 : Poisson's ratio of the inner or outer race PA1 Q.sub.d : load of a rolling element PA1 l.sub.a : effective length of the profile line of the roller. PA1 k: positive constant PA1 E.sub.1 : Young's modulus of the roller PA1 E.sub.2 : Young's modulus of the inner or outer race PA1 .nu..sub.1 : Poisson's ratio of the roller PA1 .nu..sub.2 : Poisson's ratio of the inner or outer race PA1 Q.sub.d : load of a rolling element PA1 l.sub.a : effective length of the profile line of the roller is preferably employed.
The Lundberg's expression is a theoretical expression for uniformalizing a contact stress between a plate of an infinite width and a roller, and cannot be applied as it is to the case where a raceway surface of a finite length is contacted with a roller as in the case of a roller bearing. According to studies conducted by the inventors, the followings have been found. It is preferable to use an expression which is obtained by multiplying a positive constant k and above-mentioned Lundberg's expression Zp(x), or form a gap which is indicated by EQU Z(x)=kZp(x) (2)
between a roller rolling surface and the raceway surface. It is further preferable to set the value of k to be in the range of from 1.5 to 10. These findings have been already proposed.
Both the expressions (1) and (2) based on the elastic contact theory are special logarithmic curves. In order to form a gap indicated by such a special curve between the roller rolling surface and the raceway surface of the inner or outer race, the shape of the profile line in the direction of the generating line (hereinafter, such a shape is referred to merely as "generating line shape") of at least one of the roller rolling surface and the raceway surface must be processed into a shape corresponding to such a logarithmic curve.
On the other hand, when a ground surface of a shape of a special curve is to be formed on the surface of an article, an NC (Numerically Controlled) grinding machine is usually used. Frequently, the surface of a grindstone is dressed into the negative shape of the desired curve shape by a dressing mechanism of the grinding machine, and the surface of the article is then ground.
However, a dressing mechanism of an NC grinding machine usually operates only along a linear or arcuate locus. In a practical use, therefore, it is very difficult to, in order to obtain a gap indicated by a logarithmic curve of the above-mentioned expression (1) or (2), grind the generating line shape of the rolling surface of the roller or the raceway surface of the inner or outer race, into the shape of the desired logarithmic curve.